Stereospecific construction of stereogenic vicinal quaternary carbon atoms. Enantiospecific synthesis of (+)-valerane

Stereo- and enantiospecific synthesis of (+)-valerane starting from R-carvone utilising orthoester Claisen rearrangement and intramolecular diazo ketone cyclopropanation reactions for the construction of the two vicinal quaternary carbon atoms is described. Copyright (C) 1996 Elsevier Science Ltd.

Synthetic studies directed towards the potent cytotoxic natural product ottelione A: stereoselective construction of the complete framework

A stereoselective strategy for the rapid acquisition of the complete framework (dideoxyottelione A) of the promising cytotoxic agent ottelione A, with four contiguous stereogenic centres on a hydrindane skeleton and a sensitive 4-methylenecyclohex-2-enone functionality, from the readily available Diels-Alder adduct of 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadiene and norbornadiene, is delineated.

Synthetic studies towards novel terpenic natural products kelsoene and poduran: Construction of the complete 4-5-5-fused tricarbocyclic core

A common synthetic approach to the recently reported sesquiterpene kelsoene 1 and the tetraterpene poduran 5, bearing a novel tricyclo[6.2.0.0(2,6)]decane framework, from commercially available 1,5-COD and leading to the first construction of the carbocyclic core present in these natural products is delineated.

A facile regioselective construction of spiro epoxy-bridged tetrahydropyranone frameworks

Investigations on the reactivity profile of the transient five-membered-ring cyclic carbonyl ylides, generated from alpha-diazo ketones, in the presence of the C=O group of various simple ketones and symrnetrical/unsymmetrical 1,2-diones were carried out. The reaction of alpha-diazo ketones with 1,2-naphthoquinone furnished interesting diastereomeric cycloadducts in which both the C=O groups acted as dipolarophilic sites. The similar reaction in the presence of several isatin derivatives afforded novel spiro dioxa-bridged indole derivatives as a mixture of diastereomers. The single crystal X-ray structure analysis manifestly revealed the mode of cycloaddition and the stereochemistry of two of the diastereomers. A diverse set of novel spiro epoxy-bridged tetrahydropyranone frameworks have been constructed in good yield via the tandem cyclization-cycloaddition of alpha-diazo ketones with the C=O group as heterodipolarophile in a regioselective manner. (C) 2003 Elsevier Ltd. All rights reserved.

Synthesis based on cyclohexadienes Part 36: an efficient methodology for the construction of spiro[4.5]decanes: a formal synthesis of acorone

An efficient strategy for the contruction of spiro[4.5] decanes is described and involves a bridgehead substitution of a methoxyl group by a methyl group followed by an oxidative cleavage of the tricyclo[5.2.2.0(1,5)] undecane 25 to produce the spiro[4.5] decanes 31 & 32 which are intermediates in the synthesis of acorone. A novel one-pot conversion of alpha-methoxy carboxylic acid to alpha-methyl carboxylic acid is described.

Self-organization of multiple components in a steroidal hydrogel matrix: design, construction and studies on novel tunable luminescent gels and xerogels

The present work combines two rapidly growing research areas-functional supramolecular gels and lanthanide based hybrid materials. Facile hydrogel formation from several lanthanide(III) cholates has been demonstrated. The morphological and mechanical properties of these cholate gels were investigated by TEM and rheology. The hydrogel matrix was subsequently utilized for the sensitization of Tb(III) by doping a non-coordinating chromophore, 2,3-dihydroxynaphthalene (DHN), at micromolar concentrations. In the mixed gels of Tb(III)-Eu(III), an energy transfer pathway was found to operate from Tb(III) to Eu(III) and by utilizing this energy transfer, tunable multiple-color luminescent hydrogels were obtained. The emissive properties of the hydrogels were also retained in the xerogels and their suspensions in n-hexane were used for making luminescent coating on glass surface.

Fast edge splitting and Edmonds' arborescence construction for unweighted graphs

Given an unweighted undirected or directed graph with n vertices, m edges and edge connectivity c, we present a new deterministic algorithm for edge splitting. Our algorithm splits-off any specified subset S of vertices satisfying standard conditions (even degree for the undirected case and in-degree ≥ out-degree for the directed case) while maintaining connectivity c for vertices outside S in Õ(m+nc2) time for an undirected graph and Õ(mc) time for a directed graph. This improves the current best deterministic time bounds due to Gabow [8], who splits-off a single vertex in Õ(nc2+m) time for an undirected graph and Õ(mc) time for a directed graph. Further, for appropriate ranges of n, c, |S| it improves the current best randomized bounds due to Benczúr and Karger [2], who split-off a single vertex in an undirected graph in Õ(n2) Monte Carlo time. We give two applications of our edge splitting algorithms. Our first application is a sub-quadratic (in n) algorithm to construct Edmonds' arborescences. A classical result of Edmonds [5] shows that an unweighted directed graph with c edge-disjoint paths from any particular vertex r to every other vertex has exactly c edge-disjoint arborescences rooted at r. For a c edge connected unweighted undirected graph, the same theorem holds on the digraph obtained by replacing each undirected edge by two directed edges, one in each direction. The current fastest construction of these arborescences by Gabow [7] takes Õ(n2c2) time. Our algorithm takes Õ(nc3+m) time for the undirected case and Õ(nc4+mc) time for the directed case. The second application of our splitting algorithm is a new Steiner edge connectivity algorithm for undirected graphs which matches the best known bound of Õ(nc2 + m) time due to Bhalgat et al [3]. Finally, our algorithm can also be viewed as an alternative proof for existential edge splitting theorems due to Lovász [9] and Mader [11].

Design enhancement of the underwater noise control linings through a parsimonious parametric study

Control of sound transmission through the structure and reflection from the structure immersed in fluid media impose highly conflicting requirements on the design of the carpeted noise control linings. These requirements become even more stringent if the structure is expected to be moving with considerable speed particularly under intense hydrostatic pressure. Numerous configurations are possible for designing these linings. Therefore, in this paper, a few lining configurations are identified from the literature for parametric study so that the designer is provided with an environment to analyze and design the lining. A scheme of finite element analysis is used to analyze these linings for their acoustic performance. Commercial finite element software, NISA®, is used as a platform to develop a customized environment wherein design parameters of different configurations can be varied with consistency checks and generate the finite element meshes using the 8-noded hexahedral element. Four types of designs proposed and analysed here address the parameters of interest such as the echo reduction and the transmission loss. Study of the effect of different surface distributions of the cavities is carried out. Effect of static pressure on different designs is reported.

An O(mn) Gomory-Hu Tree Construction Algorithm for Unweighted Graphs

We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V,E). The expected running time of our algorithm is Õ(mc) where |E| = m and c is the maximum u-vedge connectivity, where u,v ∈ V. When the input graph is also simple (i.e., it has no parallel edges), then the u-v edge connectivity for each pair of vertices u and v is at most n-1; so the expected running time of our algorithm for simple unweighted graphs is Õ(mn).All the algorithms currently known for constructing a Gomory-Hu tree [8,9] use n-1 minimum s-t cut (i.e., max flow) subroutines. This in conjunction with the current fastest Õ(n20/9) max flow algorithm due to Karger and Levine [11] yields the current best running time of Õ(n20/9n) for Gomory-Hu tree construction on simpleunweighted graphs with m edges and n vertices. Thus we present the first Õ(mn) algorithm for constructing a Gomory-Hu tree for simple unweighted graphs.We do not use a max flow subroutine here; we present an efficient tree packing algorithm for computing Steiner edge connectivity and use this algorithm as our main subroutine. The advantage in using a tree packing algorithm for constructing a Gomory-Hu tree is that the work done in computing a minimum Steiner cut for a Steiner set S ⊆ V can be reused for computing a minimum Steiner cut for certain Steiner sets S' ⊆ S.

Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].